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Cost of Capital Risk Analysis

- MBA Fellows
- Corporate Finance Learning Module
- Part II

Class Topics

- Incorporating risk in Capital Budgeting
- Cost of Capital Components cost of debt,

preferred stock, common equity. - Calculating the Weighted Average Cost of Capital

(WACC) - Capital Structure Decisions
- EVA

Capital Budgeting and Risk

- Prior discussion of alternative projects assumed

that the level of risk associated with each

project was the same. - How do you evaluate projects when they have

different levels of risk?

Project Risk

- Reflects the the potential variability of

returns. - Portfolio effect - if a projects proposed

returns are not perfectly correlated with the

returns from the firms other projects. - Diversification - influences risk. The total

risk of the firm may be reduced by accepting the

proposed project, if its returns are not

perfectly correlated with the returns from the

firms other investments.

Types of Project Risk

- Stand-alone Risk
- Corporate/Within Firm Risk
- Market/Beta Risk
- All Risk is not equal - some risk can be

diversified away, and some cannot.

Stand-Alone Risk

- The risk associated with a particular project,

ignoring the firms other projects/assets and

firm/shareholder diversification. - Measured by the ? (standard deviation) or CV

(coefficient of variation) of NPV, IRR, or MIRR. - Methods for estimating stand-alone risk

Sensitivity Analysis, Scenario Analysis, Monte

Carlo Simulation

Stand-alone risk

- Stand-alone risk is easiest to measure, more

intuitive. - Core projects are highly correlated with other

assets, so stand-alone risk generally reflects

corporate risk. - If the project is highly correlated with the

economy, stand-alone risk also reflects market

risk.

Coefficient of Variation (COV)

- COV is a relative measure of stand-alone risk

used. It used to compare the risk of 2 or more

assets because it enables us to choose between 2

investments when one has a higher expected rate

of return, but the other has a lower standard

deviation. - It measures the the risk per unit of return.
- COV Standard Deviation
- Expected Return

Measuring Stand-Alone Risk

- Entails determining
- the uncertainty inherent in the projects cash

flows. - the nature of the individual cash flow

distributions and their correlations with each

other to determine the nature of the NPV

probability distribution.

Probability Density

Flatter distribution, larger ?,

larger stand-alone risk.

NPV

0 E(NPV)

Corporate Risk

- The risk that the project contributes to the firm

as a whole (the effect of the project on the

earnings and cash flow variability of the firm). - Corporate risk considers the fact that some of

the project's risk will be diversified away

when the project is combined with the firms

other projects. - However, corporate risk ignores shareholder

diversification. - Depends on the projects ?, and its correlation

with returns on the firms other projects. - Measured by the projects beta.

Profitability

Project X

Total Firm

Rest of Firm

0

Years

1. Project X is negatively correlated to

firms other assets. 2. If r lt 1.0, some

diversification benefits. 3. If r 1.0, no

diversification effects.

Market Risk

- The effect (risk) of the project on a well

diversified stock portfolio. - It takes in consideration the stockholders other

assets (investments). - Depends on projects ? and its correlation with

the stock market. - Measured by the projects market beta.

Variables that Influence a Projects NPV and IRR

- Market Size
- Selling Price
- Market Growth Rate
- Market Share (unit volume sales)
- Residual Value of Investment
- Operating/Fixed Costs
- Investment required

Sensitivity Analysis

- Answers the question what if
- Shows how changes in one variable affects NPV or

IRR. - The value of one variable is changed while

holding all other variables constant. - Provides some idea of stand-alone risk.
- Provides breakeven information.

Why is sensitivity analysis useful?

- Provides some idea of stand-alone risk.
- Identifies dangerous variables.
- Provides breakeven information.

Sensitivity Analysis

- Each variable is changed by several percentage

points above and below its expected value (while

holding the other variables constant). - Then a new NPV is calculated using each of these

values. - Finally the set of NPVs is plotted against the

variable that was changed.

Example

Change from Base Level Change from Base Level Resulting NPV (000s) Resulting NPV (000s) Resulting NPV (000s) Resulting NPV (000s) Resulting NPV (000s)

Change from Base Level Change from Base Level Unit Sales Unit Sales Salvage Salvage k

-30 10 78 105

-20 35 80 97

-10 58 81 89

0 82 82 82

10 105 83 74

20 129 84 67

30 153 85 61

NPV (000s)

Unit Sales

Salvage

82

k

-30 -20 -10 Base 10 20

30 Value

Sensitivity Analysis

- Slope of the lines in the graphs show how

sensitive NPV is to changes in each of the

inputs. - The steeper the slope, the more sensitive the NPV

is to a change in the variable. - Comparison of 2 projects - the one with the

steeper slope (sensitivity lines) would be

riskier, because for that project a relatively

small error in estimating a variable would

produce a large change in the projects expected

NPV.

Results of Sensitivity Analysis

- Steeper sensitivity lines show greater risk.

Small changes result in large declines in NPV. - Unit sales line is steeper than salvage value or

k, so for this project, should worry most about

accuracy of sales forecast.

Weaknesses ofSensitivity analysis

- Does not reflect diversification.
- Says nothing about the likelihood of change in a

variable, i.e. a steep sales line is not a

problem if sales arent expected to fall. - Ignores the relationships among variables.

Scenario Analysis

- Considers both the sensitivity of NPV to changes

in key variables and identifies the range of

possible outcomes under the worst, best, and most

likely case. - It considers the impact of simultaneous changes

in key variables on the project. - It provides a range of possible outcomes.

Scenario Analysis

- Standard Deviation of NPV
- Coefficient of Variation
- CVNPV

Scenario Analysis

- The projects COV can be compared with the COV of

the companys average project to get an idea of

the relative riskiness of the project under

consideration. - Although scenario analyze can provide useful

information about a projects stand alone risk,

it is limited because it only considers a few

discrete outcomes (NPVs), even though there can

be an infinite amount of possibilities.

Assume all variables are known with certainty

except unit sales, which could range from 900 to

1,600.

Scenario Probability NPV(000)

Worst 0.25 15

Base 0.50 82

Best 0.25 148

E(NPV) 82 ?(NPV) 47 CV(NPV)

?(NPV)/E(NPV) 0.57

If the firms average project has a CV of 0.2 to

0.4, is this a high-risk project? What type of

risk is being measured?

- Since CV 0.57 gt 0.4, this project has high

risk. - CV measures a projects stand-alone risk. It

does not reflect firm or stockholder

diversification.

Would a project in a firms core business likely

be highly correlated with the firms other assets?

- Yes. Economy and customer demand would affect

all core products. - But each product would be more or less

successful, so correlation lt 1.0. - Core projects probably have correlations within a

range of 0.5 to 0.9.

How do correlation and ? affect a projects

contribution to corporate risk?

- If ?P is relatively high, then projects

corporate risk will be high unless

diversification benefits are significant. - If project cash flows are highly correlated with

the firms aggregate cash flows, then the

projects corporate risk will be high if ?P is

high.

Would correlation with the economy affect market

risk?

- Yes.
- High correlation increases market risk (beta).
- Low correlation lowers it.

Subjective risk factors should also be considered

- A numerical analysis may not capture all of the

risk factors inherent in the project. - For example, if the project has the potential for

bringing on harmful lawsuits, then it might be

riskier than a standard analysis would indicate.

Weaknesses of Scenario Analysis

- Only considers a few possible out-comes.
- Assumes that inputs are perfectly correlated--all

bad values occur together and all good values

occur together. - Focuses on stand-alone risk, although subjective

adjustments can be made.

Monte Carlo Simulation

- A computerized version of scenario analysis.
- Computer randomly selects a value for each

variable and combines these values to determine

the NPV/IRR of the project. - The process is repeated many times (1,000 or

more) until a probability distribution of the

projects NPVs/IRRs is developed with its own

expected value and standard deviation.

Monte Carlo Simulation

- The inputs to a simulation include all of the

principal factors affecting the projects

profitability, and the simulation output is a

probability distribution of NPVs or IRRs for the

project. - The project is accepted if the decision maker

feels that enough of the distribution lies above

the normal cutoff criteria (NPV gt0) or (IRRgt

Required Rate of Return).

Simulation Results (1000 trials)

- Units Price NPV
- Mean 1260 202 95,914
- St. Dev. 201 18 59,875
- CV 0.62
- Max 1883 248 353,238
- Min 685 163 (45,713)
- Prob NPVgt0 97

Interpreting the Results

- Inputs are consistent with specified

distributions. - Units Mean 1260, St. Dev. 201.
- Price Min 163, Mean 202, Max 248.
- Mean NPV 95,914. Low probability of negative

NPV (100 - 97 3).

Histogram of Results

Probability Density

x x x x x x x x x x x x x x x x x x x x x x x x

x x x x

x x x x x x x

x x x x x x x x x x x

x x x x x x x x x x x x x x x x x x x x x x x x x

0 E(NPV) NPV

Also gives ?NPV, CVNPV, probability of NPV gt 0.

Advantages of Monte Carlo Simulation

- Reflects the probability distributions of each

input. - Shows range of NPVs, the expected NPV, ?NPV, and

CVNPV. - Gives an intuitive graph of the risk situation.

Weaknesses of simulation

- Difficult to specify probability distributions

and correlations. - If inputs are bad, output will be badGarbage

in, garbage out.

Project Risk Analysis

- Sensitivity, scenario, and simulation analyses do

not provide a decision rule. They do not

indicate whether a projects expected return is

sufficient to compensate for its risk. - Sensitivity, scenario, and simulation analyses

also ignore diversification. As a result, they

measure only stand-alone risk, which may not be

the most relevant risk in capital budgeting.

Risk Adjusted Discount Rate

- Calculate the NPV of a project, using a discount

rate that has been adjusted for the riskiness of

the project. - Risk premiums applied to individual projects are

chosen in a subjective manner. - Projects assigned to risk classes and then the

same discount rate is assigned to all projects in

each class.

Cost of Capital

- Capital amount of money raised by a corporation

from creditors and investors through the issuance

of bonds (debt), preferred stock, and/or common

stock. - Cost the rate of return required by investors

and creditors who supply capital to the firm, or - The cost to the corporation of raising funds from

investors and/or creditors, or - The minimum rate of return required on new

investments undertaken by the firm.

Capital Structure

- The proportion of a firms total assets financed

by debt, preferred stock, and common stock. - Component cost - the required rate of return on

each source of capital (debt, preferred stock,

common stock) - Target Capital Structure - percentages are set

for different financing sources.

Weighted Average Cost of Capital (WACC)

- The average (after-tax) cost of the sources of

capital weighted by the proportion of each

component in the firms capital structure. - EVA - firms create value if their income exceeds

the cost of capital used to finance their

operations. - For a project to be accepted, it must generate a

return greater than its WACC.

WACC

- The WACC is based on the weighted costs of the

individual components of capital. The weights

are equal to the proportion of each of the

components in the target capital structure. - The appropriate component costs to use are the

marginal costs or the costs associated with the

next dollar of capital to be raised. These may

differ from the historical costs of capital

raised in the past.

Marginal Cost of Capital

- The primary objective of managers is to maximize

shareholder value. To do this managers must

select projects that are expected to earn more

than the firms cost of capital. - To evaluate a project that requires raising and

investing new capital, managers must compare the

marginal cost of capital to the projects

expected return.

Cost of Debt

- The after-tax cost of debt is used in the

calculation of WACC because of the tax savings

that result from the deductibility of interest. - kd ( 1- Tax rate)

Component Cost of Debt

- Interest is tax deductible, so the after tax (AT)

cost of debt is - rd AT rd BT(1 - T)
- 10(1 - 0.40) 6.
- Use the nominal rate.

Cost of Preferred Stock

- The rate of return investors require on the

firms preferred stock adjusted for flotation

costs. - kps Dps/Pn
- Because of the non-deductibility of preferred

stock dividends, the cost of preferred stock is

higher than that of debt. As a result, firms

prefer to issue debt rather than from preferred

stock.

Cost of Preferred Stock

- PP 113.10 10Q Par 100 F 2

Use this formula

Picture of Preferred Stock

?

0

1

2

rps ?

...

2.50

-111.1

2.50

2.50

Cost of Common Stock (ks)

- The rate of return required by investors in the

firms common stock. - Equity capital can be raised internally through

retained earnings or through the sale of new

common. - The cost of retained earnings is the opportunity

cost, i.e. the return that investments could earn

in alternative investments.

Cost of Common Stock (ks)

- Funds generated through earnings can either be

paid out as dividends or retained to be reinvest

them in the firm. - If the funds are paid out as dividends,

stockholders can reinvest these dividends

elsewhere to earn an appropriate rate of return. - The cost of internal equity to the firm is less

than the cost of new common stock, because the

sale of new stock requires the payment of

flotation costs.

Two ways to determine the cost of equity, ks

1. Capital Asset Pricing Model ks kRF (kM -

kRF)b kRF (RPM)b. 2. Dividend Growth Model ks

D1/P0 g

Capital Asset Pricing Model

- The rate of return investors require on the

firms common stock is a function of the risk

free rate (kRF Treasury Bond rate), the market

risk premium, and the firms beta. - rs rRF (RPM )bi
- Equity/Market Risk Premium RPM (rM - kRF)
- The additional return that investors require to

invest in risky equities.

Estimating Beta

- Run a regression with returns of the stock in

question plotted on the Y axis and returns on the

market portfolio plotted on the X axis. - Historical beta based on the past relationship

between a stocks return and the returns of the

market portfolio.

Cost of equity based on the CAPM

- rRF 7, RPM 6, b 1.2
- rs rRF (rM - rRF )b.
- 7.0 (6.0)1.2 14.2.

Dividend Growth Model

- ks D1/P0 g
- D1 - dividend to be paid next year
- P0 - current price of the stock
- g - expected growth rate of dividends
- g (Retention Rate)(ROE) or
- g (1- Payout Ratio)(ROE)

Dividend Growth Model

- Future dividends are assumed to grow at a

constant rate. - Payout ratio - the proportion of earnings (net

income) paid out in the form of dividends. - Retention rate - the proportion of earnings not

paid out as dividends (i.e. retained and

reinvested in the firm).

Whats the DCF cost of equity, rs?Given D0

4.19P0 50 g 5.

Weighted Average Cost of Capital

- WACC wdkd(1-T) wpskps wceks
- Represents the average cost of each new or

marginal dollar of capital supplied. - Percentage capital components (wd, wps, wce) are

based on accounting book values, current market

values of the components, or the targeted capital

structure.

Determining WACC

- 1) Calculate the cost of capital for each

individual component. - kd ( 1- Tax rate),
- kps Dps/Pn
- ks D1/P0 g
- 2) Compute the weighted (marginal) cost of

capital for each increment of capital raised.

Factors Affecting WACC

- Interest Rates
- Market Risk Premium
- Tax Rates
- Capital Structure Policy
- Dividend Policy
- Investment Policy

Estimating Project Risk

- The (marginal) cost of capital is a function of

projects risk. - The firms WACC is closely related to the degree

of risk associated with new investments, existing

assets, and the firms capital structure. - The 3 risks associated with a project are
- Stand-alone risk
- Corporate or with-in firm risk
- Market or beta risk

Divisional Beta

- Security Market Line - expresses the risk return

trade-off - ks kRF (kM - kRF)bi
- bi - the beta of a division.
- ks - required rate of return on the divisions
- investment.

Estimating Project Risk

- Stand Alone risk - the projects diversifiable

risk. It is measured by the variability of the

projects expected returns. - Corporate/Within Firm Risk - the projects

contribution to the firms overall risk (the fact

that the project represents only one of the

firms portfolio of assets. It is measured by the

projects impact on uncertainty about the firms

future earnings.

Estimating Project Risk

- Market/Beta Risk - project's risk as viewed by

the a well diversified stockholder who recognizes

that the project is only one of the firms assets

and that the firms tock is but one part of the

investors total portfolio. - Measures by the projects impact on the firms

beta. - Market Risk directly affects the stock prices.

CAPM and Project Risk

- Using the CAPM to estimate a projects risk

adjusted cost of capital - kproject kRF (kM - kRF)bproject

Capital Asset Pricing Model

- Market (systematic) risk is the only relevant

risk for capital budgeting purposes. - Firm can be viewed as a portfolio of assets, each

having its own beta. - The beta of a firm is the weighted average betas

of its individual assets.

Mistakes in Estimating WACC

- Using the current cost of debt instead of the

interest rate on new debt. - Using the historical average rate return on

stocks instead of the current expected rate of

return on stocks to estimate the risk premium. - If the targeted capital structure is unknown use

the market values to obtain the weights.